Question Detail

If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

1
10
100
1000

Answer: Option D

Explanation:

We know that \begin{aligned} (11)^2 = 121
\end{aligned}
So, putting values in said equation we get,
\begin{aligned} (11-1)^{2 + 1} = (10)^3 = 1000 \end{aligned}

1. Find the value of,
\begin{aligned}
\frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}}
\end{aligned}

Answer: Option C

2. \begin{aligned}
\text{If }x = \left(8 + 3\sqrt{7}\right),\text{ what is the value of }\\\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)?
\end{aligned}

\begin{aligned} \sqrt{13} \end{aligned}
\begin{aligned} \sqrt{14} \end{aligned}
\begin{aligned} \sqrt{15} \end{aligned}
\begin{aligned} \sqrt{16} \end{aligned}

Answer: Option B

Explanation:

\begin{align}&\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)^2\\\\
&= x - 2 + \dfrac{1}{x}\\\\
&= x + \dfrac{1}{x} - 2 \\\\
&= \left(8 + 3\sqrt{7}\right) + \dfrac{1}{\left(8 + 3\sqrt{7}\right)} - 2 \\\\
&= \left(8 + 3\sqrt{7}\right) + \dfrac{\left(8 - 3\sqrt{7}\right)}{\left(8 + 3\sqrt{7}\right)\left(8 - 3\sqrt{7}\right)} - 2 \\\\
&= \left(8 + 3\sqrt{7}\right) + \dfrac{\left(8 - 3\sqrt{7}\right)}{8^2 - \left(3\sqrt{7}\right)^2} - 2 \\\\
&= \left(8 + 3\sqrt{7}\right) + \dfrac{\left(8 - 3\sqrt{7}\right)}{64 - 63} - 2 \\\\
&= \left(8 + 3\sqrt{7}\right) + \dfrac{\left(8 - 3\sqrt{7}\right)}{1} - 2 \\\\
&= 8 + 3\sqrt{7} + 8 - 3\sqrt{7} - 2 \\\\
&= 14 \\\\
&\text{as }\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)^2 = 14\\\\
&\text{so ,}\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right) = \sqrt{14}\end{align}

3. If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

1
10
100
1000

Answer: Option D

Explanation:

We know that \begin{aligned} (11)^2 = 121
\end{aligned}
So, putting values in said equation we get,
\begin{aligned} (11-1)^{2 + 1} = (10)^3 = 1000 \end{aligned}

4. \begin{aligned}
\text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\
\text{ then find the value of x }
\end{aligned}

Answer: Option D

Explanation:

\begin{aligned}3^{x-y} = 27 = 3^3 <=> x-y = 3 \text{... (i)}\\
3^{x+y} = 243 = 3^5 <=> x+y = 5 \text{... (ii)} \\

\text{ adding (i) and (ii)}
=> 2x = 8 \\
=> x = 4
\end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2

\end{aligned}

Answer: Option C

Question Detail

If m and n are whole numbers such that \begin{aligned} m^n=121 \end{aligned} , the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

1. Find the value of, \begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}

2. \begin{aligned} \text{If }x = \left(8 + 3\sqrt{7}\right),\text{ what is the value of }\\\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)? \end{aligned}

3. If m and n are whole numbers such that \begin{aligned} m^n=121 \end{aligned} , the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

4. \begin{aligned} \text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\ \text{ then find the value of x } \end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}

If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

1. Find the value of,
\begin{aligned}
\frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}}
\end{aligned}

2. \begin{aligned}
\text{If }x = \left(8 + 3\sqrt{7}\right),\text{ what is the value of }\\\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)?
\end{aligned}

3. If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is

4. \begin{aligned}
\text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\
\text{ then find the value of x }
\end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2

\end{aligned}